Number System
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Q.

2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then $ab =$

 A.

10

 B.

25

 C.

52

 D.

65

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Solution:
Option(C) is correct

We have given that the number $2ab5$ is divisible by 25.

Any number divisible by 25 ends with the last two digits 00, 25, 50, or 75.
So, $b5$ should equal 25 or 75.

Hence, $b = 2$ or $7$.
Since $a$ is now free to take any digit from 0 through 9, $ab$ can have multiple values.

We also have that $ab$ is divisible by 13.
The multiples of 13 are $13, 26, 39, 52, 65, 78$ and $491$.

Among these, the only number ending with 2 or 7 is 52.

Hence, $ab=52$


(1) Comment(s)


Shobia
 ()

from the question we can clearly understand that ab is a multiple of 13,,

so from the above 4 option 52 is only a multiple of 13.

so ans:52